Ray Allen’s take: Celtics fans appreciate him for contributions more than despise him for joining rival Heat

The Garden’s Jumbotron played back the memories in the first quarter: that sugary-sweet shooting stroke; that lightning release; that warm smile; that day when the Big Three was first assembled; that day when they brought this city a championship.

When the tribute video started to roll Sunday, loud boos rained down. Yet, as it continued, applause started to build, then cheers, and then the crowd rose to its feet.

Ray Allen noticed this stark transition and translated it to mean that Boston fans ultimately appreciate his time here more than they despise him for leaving to join a bitter rival.

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“We all have history together,” Allen said after making his first trip back to the Garden since leaving the Celtics last year to sign with the Miami Heat.

“That always comes to the forefront. It always surfaces. People remember the great times, and those times are a part of my life, they’re a part of my family, they’re a part of who I am.”

But when Allen, who played with the Celtics for five seasons starting in 2007, actually checked into the game, the niceties ended.

“I didn’t expect to get booed the whole time, throughout the game, that I touched the ball,” said Allen, who had 21 points after making 7 of a season-high 17 shots in 38 minutes.

“That was interesting.”

And booed he was. The only cheers he received from then on were for missed shots.

But near the end of regulation, with his new team trailing his former team, the NBA’s all-time leader in 3-point field goals buried another from long distance to give the Heat a 78-77 lead with 4:38 left.

And when Boston seemed like it might pull away for a win, Allen hit another clutch 3-pointer with 25.1 seconds left that pulled the Heat to within a point.

Was their former teammate going to beat them in their old building? This seemed possible for the Celtics, but this never came to pass, as they held on to win in double overtime, 100-98.

When the game ended, Allen sat down and reflected.

He described experiencing “a sense of calmness when I got here, just knowing that I’m always a New Englander. That doesn’t change.”

But the walk to the visitor’s locker room was one Allen called “very weird.”

“It’s been a long time since I’ve been on that side of the hallway,” he said.

When the tribute video played, Allen said “all those emotions came streaming back from all the great things we did here.”

Heat star LeBron James said he was surprised to see a tribute video playing at all.

“But this is a class organization,” James said of the Celtics, “and I was happy for Ray and I bet his family was happy as well.”

Before the game, Celtics coach Doc Rivers reiterated how he never wanted Allen to leave — and that he was never upset that Allen joined one of Boston’s rivals.

“Listen, I wanted him to stay here, but if you’re going to leave – [Miami is] a pretty good place to go: 80 degrees, no state taxes, and playing with three pretty good, young players.”

Allen signed with Miami not long after the Celtics began courting Jason Terry, another 3-point specialist at shooting guard. There were also reports of a decayed relationship with Rajon Rondo, among other issues.

In the end, Allen turned down a three-year deal from Boston in favor of South Beach.

“I had to decide what was best for my family,” Allen said. “I’ll tell you, it was disappointing for us to have to go, but we had to make that decision. It’s unfortunate. We loved this place. We loved playing here. But circumstances presented themselves to us in the way that they did, and we had to move on.”

Allen stressed that he has no “bad blood” for anyone involved with the Celtics and that the organization has always been good to him and his family.

And through the boos and cheers Sunday, through the very weird and interesting, the sense of calmness and strangeness of walking to the other side of the hall, Allen seemed sure of at least one thing:

“I know that I’ll always be a Celtic in my mind, no matter what anybody else says.”

Baxter Holmes can be reached at baxter.holmes@globe.com. You can follow him on Twitter at @BaxterHolmes.